Symmetric edge-decompositions of hypercubes

We call a set of edgesE of the n-cubeQ _n a fundamental set for Q _n if for some subgroupG of the automorphism group ofQ _n , theG-translates ofE partition the edge set ofQ _n .Q _n possesses an abundance of fundamental sets. For example, a corollary of one of our main results is that if |E| =n and the subgraph induced byE is connected, then if no three edges ofE are mutually parallel,E is a fundamental set forQ _n . The subgroupG is constructed explicitly. A connected graph onn edges can be embedded intoQ _n so that the image of its edges forms such a fundamental set if and only if each of its edges belongs to at most one cycle.We also establish a necessary condition forE to be a fundamental set. This involves a number-theoretic condition on the integersa _j (E), where for 1 j n, a _j (E) is the number of edges ofE in thej ^th direction (i.e. parallel to thej ^th coordinate axis).     

Flow-injection chemical vapor-generating procedure for the determination of Au by atomic absorption spectrometry

Volatile Au species in an acidified medium were generated at room temperature by reduction with NaBH4 in acidified aqueous medium using a flow-injection chemical vapor-generation atomic absorption spectrometric (FI-CVG-AAS) system in the presence of micro amounts of sodium diethyldithiocarbamate (DDTC). Precision of 2.0% RSD (n = 11, 2.0 mg L(-1) level) was obtained at a sample throughput of 180 h(-1). A detection limit of 24 ng mL(-1) (3sigma) was obtained with 300 microL sample solution. The method was used for the determination of gold in ore sample digests, and the results obtained agreed well with those obtained by flame AAS.     

Magnetic superexchange involving the oxygen-sulfur-oxygen pathway of the sulfate ion: A Mössbauer spectroscopy and magnetic susceptibility study of Fe(2,9-di-CH3-phenanthroline) SO4

Zero-field Mössbauer spectra of powder samples of Fe(2,9-di-CH₃-phenanthroline) SO₄ over the range 1.7 to 300°K show a large (～ 3.6 mm/sec) temperature-independent quadrupole splitting corresponding to an orbital singlet ground term. The chemical isomer shift, δ_FE=O, is 1.16 mm/sec (source and absorber at 4.2°K) corresponding to six coordinate high-spin iron (II). Below 4.2°K, the compound exhibits magnetic hyperfine splitting suggesting slow relaxation and the possibility of long-range three-dimensional magnetic ordering with a critical temperature T_c such that 3.5°K < T_c < 4.2°K and an internal hyperfine field H_n = 325 kG at 1.69°K. High-field Mössbauer spectra at 300°K indicate that the principal component of the electric field gradient tensor is positive and axial. Similar spectra at 4.2°K show an absence of nuclear Zeeman splitting for applied fields up to 60 kG, and indicate that at 4.2°K the material is rapidly relaxing but with substantial magnetic polarization and a negative internal hyperfine field. The temperature dependence of the magnetic susceptibility confirms antiferromagnetic interactions with a broad maximum χ′_M at ～ 11.8°K presumably due to low-dimensionality exchange interactions (possibly one) along MOSOM chains. Least-squares fits of χ′_M^?1 versus T for T50°K indicate (Curie-Weiss behavior with C = 3.26 emu/mole, θ = -21.95°K, and μ_eff = 5.11.     

Composite poly(dimethylsiloxane)/glass microfluidic system with an immobilized enzymatic particle-bed reactor and sequential sample injection for chemiluminescence determinations

A three-layer poly(dimethylsiloxane) (PDMS)/glass microfluidic system for performing on-chip solid-phase enzymatic reaction and chemiluminescence (CL) reaction was used for the determination of glucose as a model analyte. A novel method for the immobilization of controlled-pore-glass based reactive particles on PDMS microreactor beds was developed, producing an on-chip solid-phase reactor that featured large reactive surface and low flow impedance. Efficient mixing of reagent/sample/carrier streams was achieved by incorporating chaotic mixer structures in the microfluidic channels. A conventional sequential injection (SI) system was adapted for direct coupling with the microfluidic system, and combined with hydrostatic delivery of reagents to achieve efficient and reproducible sample introduction at 10 μl levels. A detection limit of 10 μM glucose (3σ), and a precision of 3.1% RSD (n=7, 0.2 mM glucose) were obtained using the SI-microfluidic-CL system integrated with a glucose oxidase (GOD) reactor. Carryover was <5% at a throughput of 20 samples/h.     

Mathematical modeling of electromagnetic wave propagation in heterogeneous lossy coaxial cables with variable cross section

In this work, we focus on the time-domain simulation of the propagation of electromagnetic waves in non-homogeneous lossy coaxial cables. The full 3D Maxwell equations, that described the propagation of current and electric potential in such cables, are classically not tackled directly, but instead a 1D scalar model known as the telegraphist's model is used. We aim at justifying, by means of asymptotic analysis, a time-domain “homogenized” telegraphist's model. This model, which includes a nonlocal in time operator, is obtained via asymptotic analysis, for a lossy coaxial cable whose cross section is not homogeneous.     

Synthesis and characterization of fluorine-containing cholesteric liquid crystalline polysiloxanes bearing trifluoromethyl-substituted mesogens

A series of side-chain liquid crystal (LC) polysiloxanes were synthesised with Poly(methylhydrogeno)siloxane, 4?-(undec-10-enoyloxy) biphenyl – 4 – yl 4- (trifluoromethyl) benzoate (M_th) and a chiral nematic (N*) LC monomer 1-allyl 10-(cholesteryl)-decanedioate (M_ch). The chemical structures and LC properties of the monomers and polymers were characterised by FTIR, ¹H-NMR, differential scanning calorimetry, thermogravimetric analysis, POM and X-ray diffractometer. M_ch is monotropic N* LC. The homopolymer derived from monomer M_ch is enantiotropic N* LC. Monomer M_th is a smectic A liquid crystal. The copolymers derived from M_ch and M_th are N* LCs. The temperatures at which 5% weight loss occurred are greater than 300°C for all the fluoro-containing polymers, and the residue weights of the samples at 600°C increased slightly as the content of trifluoromethyl mesogens increased in the polymers. The glass transition temperatures of the polymers increased as trifluoromethyl mesogens increased, too. The N*–I phase transition temperatures show a negative deviate from ideal or linear behaviour. The values of the enthalpy changes for the cholesteryl containing polymers are rather low and this is attributed to the biaxiality of cholesteryl moiety which tends to reduce the change in the orientational order at the N*–I transition. Compared to the monomers, the polymers show wider mesophase region.     

Bounded invariant verification for time-delayed nonlinear networked dynamical systems

We present a technique for bounded invariant verification of nonlinear networked dynamical systems with delayed interconnections. The underlying problem in precise bounded-time verification lies with computing bounds on the sensitivity of trajectories (or solutions) to changes in initial states and inputs of the system. For large networks, computing this sensitivity with precision guarantees is challenging. We introduce the notion of input-to-state (IS) discrepancy of each module or subsystem in a larger nonlinear networked dynamical system. The IS discrepancy bounds the distance between two solutions or trajectories of a module in terms of their initial states and their inputs. Given the IS discrepancy functions of the modules, we show that it is possible to effectively construct a reduced (low dimensional) time-delayed dynamical system, such that the trajectory of this reduced model precisely bounds the distance between the trajectories of the complete network with changed initial states. Using the above results we develop a sound and relatively complete algorithm for bounded invariant verification of networked dynamical systems consisting of nonlinear modules interacting through possibly delayed signals. Finally, we introduce a local version of IS discrepancy and show that it is possible to compute them using only the Lipschitz constant and the Jacobian of the dynamic function of the modules.     

Effect of spacer length on mesomorphic behaviours of chiral liquid crystal compounds containing (-)-menthyl

ABSTRACT

A homologous series of new chiral liquid crystal compounds, MnBEB (n = 4–10), was prepared by covalently linking a chiral (–)-menthyl with biphenyl-benzoate via a dicarboxylic spacer of varying length and parity. A combination of analysis methods, such as FT-IR, ¹H NMR spectra, differential scanning calorimetry (DSC), polarised optical microscopy (POM) and X-ray diffraction was carried out to systematically investigate their phase structures and phase transition behaviours. The length and parity of the flexible spacers has a profound influence on the T_m and T_c and a modest odd-even effect is observed for the chiral liquid crystal compounds MnBEB. Only compound M4BEB developed an N* phase with selectively reflection on heating and a blue phase on cooling process. In addition, increasing the length of the flexible spacers tends to narrow the temperature range of the N* phase and widen the smectic phase, moreover, the pitch becomes longer with the spacer increases.     

Single crystal synthesis and magnetism of the BaLn2O4 family (Ln = lanthanide)

The series of compounds in the BaLn₂O₄ family (Ln = La–Lu, Y) has been synthesized for the first time in single crystalline form, using a molten metal flux. The series crystallizes in the CaV₂O₄ structure type with primitive orthorhombic symmetry (space group Pnma, #62), and a complete structural study of atomic positions, bonds, angles, and distortions across the lanthanide series is presented. With the exception of the Y, La, Eu, and Lu members, magnetic susceptibility measurements were performed between 2 K and 300 K. BaCe₂O₄ and BaYb₂O₄ display large crystal fields effects and suppression of magnetic ordering. All compounds show signs of magnetic frustration due to the trigonal arrangements of the trivalent lanthanide cations in the structure.